Hypothesis generation and updating in large language models

Large language models (LLMs) increasingly help people solve problems, from debugging code to repairing machinery. This process requires generating plausible hypotheses from partial descriptions, then updating them as more information arrives. Yet how LLMs perform this form of inference, and how close it is to optimal, remains unclear. We study this question in the number game, a controlled setting in which a learner infers the hypothesis supported by a few positive integers, such as $\{16, 8, 2, 64\}$: a rule like powers of 2 or an interval like numbers near 20. We measure the posterior over hypotheses using three complementary probes: posterior prediction, hypothesis evaluation, and hypothesis generation. We then compare LLM behavior with an optimal Bayesian model and human behavior, and test whether the same posterior is expressed across probes. LLMs are often well described by a two-parameter Bayesian fit, but with systematic offsets: by default they show a strong-sampling assumption that creates an implicit Occam's razor, favoring narrower hypotheses, while thinking mode shifts them toward greater prior reliance. We also find a robust evaluation--generation gap: LLMs select more correct hypotheses during hypothesis evaluation but generate simpler, more rule-like hypotheses. Finally, this Bayesian-with-bias pattern does not extrapolate. Models can behave as if they hold rule-like hypotheses over observed examples, yet generalize poorly to parts of the hypothesis domain not covered by those examples. Our results highlight a limitation of LLMs as general problem solvers, especially for scientific inference, where hypotheses must go beyond the data.

Language Models Are Capable of Metacognitive Monitoring and Control of Their Internal Activations

Large language models (LLMs) can sometimes report the strategies they actually use to solve tasks, but they can also fail to do so. This suggests some degree of metacognition -- the capacity to monitor one's own cognitive processes for subsequent reporting and self-control. Metacognitive abilities enhance AI capabilities but raise safety concerns, as models might obscure their internal processes to evade neural-activation-based oversight mechanisms designed to detect harmful behaviors. Given society's increased reliance on these models, it is critical that we understand the limits of their metacognitive abilities, particularly their ability to monitor their internal activations. To address this, we introduce a neuroscience-inspired neurofeedback paradigm designed to quantify the ability of LLMs to explicitly report and control their activation patterns. By presenting models with sentence-label pairs where labels correspond to sentence-elicited internal activations along specific directions in the neural representation space, we demonstrate that LLMs can learn to report and control these activations. The performance varies with several factors: the number of example pairs provided, the semantic interpretability of the target neural direction, and the variance explained by that direction. These results reveal a "metacognitive space" with dimensionality much lower than the model's neural space, suggesting LLMs can monitor only a subset of their neural mechanisms. Our findings provide empirical evidence quantifying metacognitive capabilities in LLMs, with significant implications for AI safety.